4. Let $w$ be the circumcircle of right-angled triangle $ABC (\angle A = 90)$. Tangent to $w$ at point $A$ intersects the line $BC$ in point $P$. Suppose that $M$ is the midpoint of (the smaller) arc $AB$, and $PM$ intersects $w$ for the second time in $Q$. Tangent to $w$ at point $Q$ intersects $AC$ in $K$. Prove that $\angle PKC = 90$.

I think we judge talent wrong. What do we see as talent? I think I have made the same mistake myself. We judge talent by the trophies on their showcases, the flamboyance the supremacy. We don't see things like determination, courage, discipline, temperament.

I think we judge talent wrong. What do we see as talent? I think I have made the same mistake myself. We judge talent by the trophies on their showcases, the flamboyance the supremacy. We don't see things like determination, courage, discipline, temperament.